Best-choice problems with disorder

1. Best-choice problems with disorder Evgeny Ivashko ivashko@krc.karelia.ru Science advisor: Prof. Vladimir Mazalov Institute of Applied Mathematical Research Karelian Research Centre Russian Academy of Sciences

2. Best-choice problems with disorder: Background 1. A. N. Shiryaev, Statistical sequential analysis, Moscow, 1976, Russian: Disorder problem The problem of the fastest finding the moment of disorder (the moment of changing the probability distribution)‏ 2. V. Mazalov, P. Neumann, I. Falco. Game of optimal stopping observations with unknown values, Chita, 1998, Russian. The best-choice game with partial information 3. M. Sakaguchi. A best-choice problem for a production system which deteriorates at a disorder time. Scienticae Mathematicae Japonicae, Vol. 54, No 1 The best-choice full-information perfect problem with disorder Karelian Research Center of the RAS, Institute of Applied Mathematical Research

3. Best-choice problems with disorder: Model Production system (PS) sequentially generates independent identical distributed random variables X1, X2, ..., XN PS in a good state (Good): Xi uniform on [0,1] PS in a bad state (Bad): Xi uniform on [0,b] Every value can be accepted or rejected Recall is not allowed Observer aims to accept the largest value Karelian Research Center of the RAS, Institute of Applied Mathematical Research

4. Best-choice problems with disorder: Main Results 1. Full-information best-choice problem with disorder (maximizing probability of success, one-threshold strategy): analitical formula of optimal thresholds for various parameters (α, b) is found; 2. Multithresholds full-information best-choice problem with disorder (maximizing expect value of accepting observation, multithresholds strategies): analitical formula of optimal thresholds for various parameters (α, b) is found; 3. Considered applications of the best-choice problem with disorder to management and defending against Denial-of-Service attacks. Karelian Research Center of the RAS, Institute of Applied Mathematical Research

5. Best-choice problems with disorder: Applications and Future plans • Applications: • Security: detecting denial-of-service attacks • Management: house-selling problem at the «hot» market • Grid tasks management: optimal-time big tasks passing to the Grid • other... • Future plans: • Imperfect best-choice game with disorder • Best-choice game with disorder and player's priorities • Law-linked multithreaded best-choice problem with disorder • Some application-specific articles Karelian Research Center of the RAS, Institute of Applied Mathematical Research

6. Best-choice problems with disorder: References 1. Vladimir V. Mazalov, Evgeny E. Ivashko Best-choice problem with disorder // Proceedings of Dynamic games and multicriteria Optimization (DGMO-2006), Petrozavodsk, September 2-7, 2006 2. Vladimir V. Mazalov, Evgeny E. Ivashko Best-choice problem with disorder // Proceedings of V Moscow International Conference on Operations Research (ORM2007), dedicated to the outstanding Russian scientists Nikita N. Moiseev 90th birthday, Moscow, April 10-14, 2007 3. Vladimir V. Mazalov, Evgeny E. Ivashko Full-information best-choice problem with disorder // Surveys in Applied and Industrial Mathematics, Vol 2, No 14, 2007, pp. 215-224 4. Evgeny E. Ivashko Multithreaded full-information best-choice problem with disorder // Proceedings of the Institute of Applied Mathematical Research, Vol 8, 2007, pp. 11-15 Karelian Research Center of the RAS, Institute of Applied Mathematical Research